c++ - creating full range of random floats using std::random -

i'm attempting test mathematical class i've created using random numbers full range of representable positivefloats, find seem having problem use of std::random. program

#include <random> #include <iostream> #include <functional>  template <typename t> class rand { public:     rand(t lo=std::numeric_limits<t>::min(),           t hi=std::numeric_limits<t>::max()) :          r(bind(std::uniform_real_distribution<>(lo, hi),std::mt19937_64{})) {}     t operator()() const { return r(); } private:     std::function<t()> r; };  int main() {     rand<float> f{};     const int samples = 1000000;     float min = std::numeric_limits<float>::max();     float max = std::numeric_limits<float>::min();     std::cout << "range min = " << max          << ", max = " << min << '\n';     (int i=0; < samples; ++i) {         float r = f();         if (r < min) min = r;         if (r > max) max = r;     }     std::cout << "for n = " << samples          << "\nsample min = " << min          << ", max = " << max << std::endl; } 

produces output

range min = 1.17549e-38, max = 3.40282e+38 n = 1000000 sample min = 8.14884e+31, max = 3.40281e+38 

clearly range extremely skewed toward larger numbers. how generate desired range of floats uniform distribution?

in addition statistics have printed out, i've computed both theoretical , actual mean, variance, skew , kurtosis of this distribution. here code, , results:

#include <random> #include <iostream> #include <functional> #include <vector> #include <numeric> #include <cmath>  template <typename t> class rand { public:     rand(t lo=std::numeric_limits<t>::min(),           t hi=std::numeric_limits<t>::max()) :          r(bind(std::uniform_real_distribution<>(lo, hi),std::mt19937_64{})) {}     t operator()() const { return r(); } private:     std::function<t()> r; };  template <class t> inline t sqr(t x) {     return x * x; }  int main() {     rand<float> f{};     const int samples = 1000000;     float min = std::numeric_limits<float>::max();     float max = std::numeric_limits<float>::min();     std::vector<float> u;     std::cout << "range min = " << max          << ", max = " << min << '\n';     (int i=0; < samples; ++i) {         float r = f();         if (r < min) min = r;         if (r > max) max = r;         u.push_back(r);     }     std::cout << "for n = " << samples          << "\nsample min = " << min          << ", max = " << max << std::endl;     double mean = std::accumulate(u.begin(), u.end(),                                           double(0)) / u.size();     double var = 0;     double skew = 0;     double kurtosis = 0;     (int = 0; < u.size(); ++i)     {         double d = (u[i] - mean);         double d2 = sqr(d);         var += d2;         skew += d * d2;         kurtosis += d2 * d2;     }     var /= u.size();     double dev = std::sqrt(var);     skew /= u.size() * dev * var;     kurtosis /= u.size() * var * var;     kurtosis -= 3;     double x_mean = ((double)min + max) / 2;     double x_var = sqr((double)max - min) / 12;     double x_skew = 0;     double x_kurtosis = -6./5;     std::cout << std::scientific << '\n';     std::cout << "            expected        actual\n";     std::cout << "mean      " << x_mean     << "       " << mean << "\n";     std::cout << "variance  " << x_var      << "       " << var << "\n";     std::cout << "skew      " << x_skew     << "       " << skew << "\n";     std::cout << "kurtosis  " << x_kurtosis << "       " << kurtosis << "\n"; } 

and here results:

range min = 1.17549e-38, max = 3.40282e+38 n = 1000000 sample min = 8.14884e+31, max = 3.40281e+38              expected        actual mean      1.701407e+38       1.700724e+38 variance  9.649275e+75       9.645774e+75 skew      0.000000e+00       7.401975e-04 kurtosis  -1.200000e+00       -1.199432e+00 

everything looking pretty me.